Alexis Rincon, right, placing flowers on the coffin of his daughter, Genesis, after a graveside service for the slain 12-year-old on Saturday.

A bullet hole.

As he walked along Rosa Parks Boulevard the other day, Martin, a 46-year-old contractor, stopped near the piece of cracked sidewalk at Warren Street where 12-year-old Genesis Rincon was shot to death a week before.

Martin gazed for a few seconds at the array of candles and teddy bears stacked against a chain link fence and covered by a blue vinyl tarpaulin. Then he shook his head and voiced a concern that many in this wounded city are now asking.

The Rincon family’s tragedy is by no means an isolated case in Paterson, as illustrated at Genesis Rincon’s funeral on Saturday. Above, Mercedes Sanchez leaning on the headstone of her son, Kuba Sanchez, who was fatally shot in the city at age 15 on Christmas Eve in 1997.

“Will this be a turning point?”

Martin paused, then answered his own question.

“I don’t know,” he said.

These are hard times in Paterson. Even before Genesis was killed and mourners gathered for a week of memorial services and rallies that culminated in her funeral on Friday and burial on Saturday, the city had already experienced a stunning surge in gun violence. In the first four months of the year, the Passaic County Prosecutor’s Office said Paterson endured three dozen shootings — about one every four days. Indeed, a 24-year-old city man was shot and critically injured early Saturday during a dispute in the parking lot of a public-housing complex, police said.

But the killing of Genesis, who was with two friends and riding a scooter on a Saturday evening of the Fourth of July weekend when she was shot in the head, startled a city that has witnessed plenty of brutality.

The new mayor, Joey Torres, who was in office from 2002 to 2010, returned to City Hall on July 1, pledging to impose curfews and beef up police patrols in dangerous neighborhoods. But how Torres plans to do that is something of a mystery — and a potential dilemma of his new administration.

Paterson was so cash-strapped in 2011 that it laid off 125 police officers — almost a quarter of its force.

Those cutbacks in the city’s police force are not likely to be reversed unless the city receives a cash windfall or cuts other services. Indeed, even today, the lack of municipal revenue still plagues the city in other ways. Torres’ plan to fill potholes — a major problem on many city streets — would require the city to borrow $37 million and increase its debt by almost 35 percent.

Such concerns, however, seem distant to the people who live near the corner of Rosa Parks Boulevard and Warren Street — and the memorial to Genesis.

Familiar violence

Here, in the heart of Paterson’s 4th Ward, violence has become an all-too-frequent part of everyday life, with the staccato pop of gunshots as a nightly drumbeat. More than half the 31 shootings from January to May of this year took place in the 4th Ward, a mile-square patch on Paterson’s north end that is home to about 13,000 of the city’s 146,000 residents.

Deborah Pierce moved into the 4th Ward only seven months ago. But Genesis’ death bothered her so much that she now wants to move out.

She does not have great hopes that life on the street will change much.

“Paterson is a decent community,” Pierce said. “But you got a bad element in Paterson.”

Her suggestion: a curfew.

“They need to lock down Paterson,” Pierce said, then quickly adding, “bring in the National Guard.”

An influx of soldiers might bring a momentary calm to the 4th Ward. But other deeply endemic social and economic problems plague the neighborhood as well as the entire city.

Almost a third of the city’s residents live below the poverty line. Federal census statistics place the city’s median income at $34,086, less than half the statewide median income of $72,999.

Unemployment in Paterson is still a double-digit problem — around 12 percent so far this year, according to state figures, or about twice the state level.

But one of the most difficult challenges, say a variety of community leaders, is raising the educational level — and job skills — of Paterson’s residents.

Only 4 percent of the city’s residents have college degrees, and just 32 percent have high school diplomas, according to the census data. Almost a quarter of the adult population entered high school but dropped out.